# Properties

 Label 90354o Number of curves 2 Conductor 90354 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("90354.n1")

sage: E.isogeny_class()

## Elliptic curves in class 90354o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.n2 90354o1 [1, 1, 1, 6132, 2008509] [] 508032 $$\Gamma_0(N)$$-optimal
90354.n1 90354o2 [1, 1, 1, -4662158, -3880171573] [] 3556224

## Rank

sage: E.rank()

The elliptic curves in class 90354o have rank $$1$$.

## Modular form 90354.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 3q^{7} + q^{8} + q^{9} + q^{11} - q^{12} + 2q^{13} - 3q^{14} + q^{16} - 7q^{17} + q^{18} - 7q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 